It's not a stupid question. The way that popular accounts "explain" quantum mechanics leads naturally to your question. The moral is that those popular accounts are not to be trusted.
Quantum mechanics is unusual in that on the one hand, we understand very well how to apply it and what we should expect to find in experiments if it's correct, but on the other hand there is sharp disagreement over what quantum mechanics is telling us about the nature of the things we use it to predict and explain. The problem you're raising comes from the superposition principle. A quantum system can be in a superposition of being in two different, non-overlapping places, for example. When that happens, there's some probability that if we "look" (make an appropriate measurement) we'll find the system in one of the places, and some probability that we'll find it in the other. However, we can't understand this as a simple case of ignorance --- as a case where the system really is in one place or really is in the other and...

I'm not sure what the difference between the philosophical and the mathematical sense of "determinism" is supposed to be, but I think that the answer will be the same in any case. And that answer is: it depends on how you think quantum theory should be understood.
On what we might describe broadly as the "orthodox interpretation" of quantum theory, the answer is no: the decay is not a deterministic event. Roughly put, this means that the state of the world before the decay doesn't determine whether the atom will decay. There are some complications here about relativity and about so-called entangled states, but we can leave them aside. On this way of looking at quantum theory, sometimes the "wave function" or "quantum state" changes unpredictably and discontinuously, and these changes are genuine chance events. Radioactive decay is a special case.
According to Bohmian mechanics, the most important of the so-called "hidden variable" views, quantum systems are thoroughly deterministic. What happens in the...

I will confess that I don't see the charm of Tegmark's view. I quite literally find it unintelligible, and I find the "advantages" not to be advantages at all.
You suggest a few possible attractions of the view. One is that "atomic and subatomic particles have only mathematical properties (mass, spin, wavelength, etc.) and hence we might as well see them as nothing but math. Any proton, for example, is quite interchangeable with any other." But first, the fact that we only have mathematical characterizations of these properties is both false and irrelevant insofar as it's true. It's false because knowing something about the mass or the spin or whatever of a particle has experimental consequences. It tells us that one thing rather than another will happen in real time in a real lab. If that weren't true, we'd have no reason to take theories that talk about these things seriously; we'd cheat ourselves of any possible evidence. Of course, we may not know what spin is "in itself," and perhaps to that...

My short answer is that we don't need to be able to visualize higher-dimensional spaces in order to reason about them. I'd be quite astonished if Stephen Hawking could visualize 11 or 26 or even 5 dimensions. In fact, visualizing even three dimensions is not as easy as people think, as one realizes when trying to think through certain "ordinary" geometrical descriptions. But there are tricks that can sometimes give you the sense of visualizing higher dimensions, as with various diagrams of a four-dimensional "hypercube." Here's an example:
https://plus.google.com/117663015413546257905/posts/VteWm45DCff
Turns out that what I've said is more or less what the well-known physicist Sean Carroll says here:
http://www.preposterousuniverse.com/blog/2009/03/30/why-cant-we-visualize-more-than-three-dimensions/
though he adds some speculations that you can evaluate for yourself. But on the question you ask, it's (1) you can't, (2) you don't need to, and (3) there are all the same some tricks.

The rule of thumb when you hear someone claim that quantum mechanics explains or underwrites something about minds is to be very, very suspicious.
Let's suppose that two particles within some microtubule get entangled. (Caveat: I know more or less nothing about microtubules, but that won't matter for what follows.) Now suppose that these particles get dispersed into spacetime. The chance that these particles will remain entangled for any significant length of time at all is near enough to zero that the difference isn't worth arguing about. That's because if anything else interacts with either particle, the entanglement will be destroyed. Entanglement is very fragile. In entanglement experiments, physicists have to go to great lengths to prevent decoherence—the process by which interaction with the environment destroys entanglement, or more accurately, disperses it into the environment, in effect diluting it.
But even if the two particles somehow stayed entangled, this wouldn't give us any special...

There's no simple uncontroversial answer to your question, but perhaps a couple of points will be at least somewhat helpful.
"Wave-particle duality" is ultimately too narrow a way to think about what you're interested in. The things that get described as illustrating "wave-particle duality" are special cases of the phenomenon of quantum interference, and that, in turn, is a manifestation of the fact that quantum states obey a superposition principle . At the end of the day, there's no substitute for thinking of this mathematically, but I'll do my best to avoid that here.
You probably know at least a bit about polarization. If we hold a polarizing filter (e.g., a lens from good sunglasses) up to a light source, the light that gets past it is polarized along a common axis—let's say the vertical axis. In principle, with the right kind of light source, we can turn the intensity down so that only one photon is emitted at a time. If such a photon passes the filter, it will hit a screen in one spot—like a...

I'm not quite as happy with Prof. Kraus's way of putting things. I'd suggest having a look at this review by philosopher/physicist David Albert:
http://www.nytimes.com/2012/03/25/books/review/a-universe-from-nothing-by-lawrence-m-krauss.html
As for whether something has always existed, Prof. Maitzen and I may well agree, but there's some ambiguity here that's worth thinking about.
If we say that something has always existed, the most plausible way to understand that is that there has never been a time when nothing existed. If there's no time before the Big Bang, then we can say that something or other has always existed.
Suppose, however, that there are times earlier than the Big Bang. One possibility is that what there was is an earlier cycle in an oscillating universe. In that case, the "something" was the sort of thing that's around in this phase of cosmic history.
Another possibility is that what was around was the vacuum of quantum field theory. The vacuum, indeed, is not matter, but it's...

I'm pretty sure that mathematicians and physicists would both reject the way you've described them.
Mathematics not only accepts the concept of infinity but has a great deal to say about it. To take just one example: Cantor proved in the 19th century that not all infinite sets are of the same size. In particular, he showed that whereas the counting numbers and the rational numbers can be paired up one-for-one, there's no such pairing between the counting numbers and the full set of real numbers. Thus, he proved that in a well-defined sense, there are more real numbers than integers, even though in that same sense there are not more rational numbers than integers.
Now of course, we sometimes talk about certain functions going to infinity in a certain limit. For example: as x goes to 0, 1/x goes to infinity, even though there is no value of x for which the value of 1/x is infinity. Rather, we say that at 0, the function is not defined. There are good reasons why we say that, though this isn't the...

I guess I'd have to disagree with the idea that "all of philosophy and logic point to a reason or cause for everything." There's certainly no argument from logic as such; it's perfectly consistent to say that some events are genuinely random. Some philosophers have held that there's a reason (not necessarily a cause in the physical sense, BTW) for everything, but the arguments are not very good.
On the other hand... quantum mechanics is a remarkably well-confirmed physical theory that, at least as standardly interpreted, gives us excellent reason to think that some things happen one way rather than another with no reason or cause for which way they turned out.
An example: suppose we send a photon (a quantum of light) through a polarizing filter pointed in the vertical direction. We let the photon travel to a second polarizing filter, oriented at 45 degrees to the vertical. Quantum theory as usually understood says that there's a 50% chance that the photon will pass this filter and a 50% chance that it...

I think it's a bit optimistic to say that physicists are close to proving the existence of a multiverse, but we can set that aside. There are different ideas of a multiverse in physical theory, but none of the ones that cosmologists take seriously call for showing that literally every possible "universe" exists. Rather, what's at stake is the idea that the totality of the Universe writ large contains relatively isolated sub-parts that have many of the characteristics of the physical universe as we usually think of it. In particular, the values of various physical "constants" would vary across the different sub-universes. But the important point for your question is that this is entirely about physics and has nothing to do with God. God, as usually understood, is not a physical being at all, but a being who (among other things) underwrites the existence of physical things. God doesn't exist within this or any other physical universe on the usual theological view. Put it another way: if the God...